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Full text of "Progressive Failure Studies of Composite Panels With and Without Cutouts"

AIAA-2001-1182 



PROGRESSIVE FAILURE STUDIES 

OF COMPOSITE PANELS 
WITH AND WITHOUT CUTOUTS 

Damodar R. Ambur* 

NASA Langley Research Center 

Hampton, VA 23681-2199 

Navin Jaunky^ 

ICASE 

Hampton, VA 23681-2199 

Carlos G. Davila^ and Mark Hilburger^ 

NASA Langley Research Center 

Hampton, VA 23681-2199 



Abstract 

Progressive failure analyses results are pre- 
sented for composite panels with and without a 
cutout and are subjected to in-plane shear load- 
ing and compression loading well into their post- 
buckling regime. Ply damage modes such as ma- 
trix cracking, fiber-matrix shear, and fiber fail- 
ure are modeled by degrading the material prop- 
erties. Results from finite element analyses are 
compared with experimental data. Good agree- 
ment between experimental data and numerical 
results are observed for most structural configu- 
rations when initial geometric imperfections are 
appropriately modeled. 

Introduction 



'Head, Mechanics and Durability Branch. Associate 
Fellow AIAA 

^Senior Staff scientist. Member AIAA 

^Aerospace Engineer, Analytical & Computational 
Methods Branch. Member AIAA 

5 Aerospace Engineer, Mechanics and Durability 
Branch. Member AIAA 

'Copyright ©2001 by the American Institute of Aero- 
nautics and Astronautics, Inc. No copyright is asserted 
in the United States under Title 17, U.S code. The U.S 
Government has a royalty-free license to exercise all rights 
under the copyright claimed herein for Government Pur- 
poses. All other rights are reserved by the copyright 
owner. 



The use of composite materials for aircraft 
primary structures can result in significant ben- 
efits on aircraft structural cost and performance. 
Such applications of composites materials are ex- 
pected to result in a 30-40 percent weight savings 
and a 10-30 percent cost reduction compared to 
conventional metallic structures. However, un- 
like conventional metallic materials, composite 
structures fail under different failure modes such 
as matrix cracking, fiber-matrix shear failure, 
fiber failure, and delamination. The initiation 
of damage in a composite laminate occurs when 
a single ply or part of the ply in the laminate fails 
in any of these failure modes over a certain area 
of the structure. The initiation of damage does 
not mean that the structure cannot carry any 
additional load. The residual load bearing capa- 
bility of the composite structure from the onset 
of material failure or initiation of damage to fi- 
nal failure can be quite significant. It is at the 
final failure load that the structure cannot carry 
any further load. This may be due to the fact 
that some failure modes may be benign not to 
degrade the performance of the overall structure 
significantly. Accurate determination of failure 
modes and their progression helps either to de- 
vise structural features for damage containment 
or to define fail-safe criteria. Therefore it is im- 
portant to understand the damage progression in 



//v^. 



.'f <.l 



composite structures subjected to different load- 
ing conditions. 

Considerable work has been performed on 
this subject. In 1987, Talreja ([1]), Allen et al. 
([2]), and Chang and Chang ([3]), independently 
proposed progressive failure models that describe 
the accumulation of damage in a composite lam- 
inate by a field of internal state variables. The 
damage model proposed by Chang and Chang 
([3]) for notched laminate loaded in tension ac- 
counts for all of the possible failure modes ex- 
cept delamination. Chang and Lessard ([4]) later 
investigated the damage tolerance of composite 
laminates subjected to compression. Davila et 
al. ([5]) extended Chang and Lessard method 
from two dimensional membrane effects to shell- 
based analysis that includes bending. Shell-based 
progressive failure analyses that apply a mate- 
rial degradation model at every material point 
in every ply in the laminate have been reported 
in References [6] through [9]. Recently a shell- 
based progressive failure analysis which consid- 
ered large rotations based on a total Lagrangian 
approach method was presented in Reference 
[10]. 

The objective of the. present paper is to de- 
velop and validate an efficient methodology that 
can predict the ultimate strength of compos- 
ite panels by taking into account ply damage 
modes and geometrical non-linear response. Re- 
sults from progressive failure analyses of compos- 
ite panels with and without a cutout subjected to 
shear and compressive loads are compared with 
experimental results. In this paper progressive 
failure results are compared with experimental 
results for flat panels with and without cutout 
subjected in-plane shear loading. Progressive 
failure results are also presented for curved panels 
with and without a cutout and subjected to ax- 
ial compression. Although results from such ex- 
perimental studies have been compared by other 
authors with postbuckling cuialyses results, pro- 
gressive failure analyses for nonlinearly deformed 
structures is not reported in the open literature. 
Thus another objective for this paper is to pro- 
vide such a comparison. 

Failure Analysis 

Failure modes in laminated composite panels 
are strongly dependent on ply orientation, load- 
ing direction and panel geometry. There are four 
basic modes of failure that occur in a laminated 
composite structure. These failure modes are; 
matrix cracking, fiber-matrix shear failure, fiber 



failure, and delamination. Delamination failure, 
however, is not included in the present studies. In 
order to simulate damage growth accurately, the 
failure analysis must be able to predict the fail- 
ure mode in each ply and apply the corresponding 
reduction in material stiffnesses. The failure cri- 
teria included in the present analyses are those 
proposed by Hashin [11] and are summarized be- 
low. 

• Matrix failure in tension and compression 
occurs due to a combination of transverse, 
iT22, and shear stress, T12, na and t-23- The 
failure index can be defined in terms of 
these stresses and the strength parame- 
ters Y and shear allowables Sc- Failure 
occurs when the index exceeds unity. As- 
suming linear elastic response, the failure 
index has the form: 



e' = 



-i- 



CT22 
Yc 



and 



„2 _ 



-I- 



T12 
Scl2 

T23 
•5c23 



CT22 

Yt 

T23 

Sc23 



25c23 
2 

+ 



1 



+ 



(72 2 



25, 



c23 



Tl3 



5cl3 



for (T22 < 



(1) 



-I- 



T12 



'cl2 



Tl3 



'cl3 



for 022 > 



(2) 



where Yt is the strength perpendicular to 
the fiber direction in tension, Yc is the 
strength perpendicular to the fiber direc- 
tion in compression, and Scu, Sci3, and 
5c23 are the in-plane shear, and transverse 
shear strengths, respectively. 

• Fiber-matrix shear failure occurs due to a 
combination of axial stress (cru) and the 
shear stresses. The failure criterion has 
the form: 



e' = 



Ac/ \^cV2 

2 



(^) for an < (3) 

\Jc\.3 J 



and 



el = 



Scl2 



+ (~) for an > (4) 

\Ocl3/ 



where A'( is the strength along the fiber 
direction in tension, and Xc is the strength 
along the fiber direction in compression. 

• Fiber failure occurs due to tension or com- 
pression independent of the other stress 
component. In compression the fiber fails 
by buckling. The failure criterion has the 
form: 

6/ = -^ for an < (5) 



and 



e/ = 



^11 
Xt 



for an > 



(6) 



To simulate the above failure modes, the 
elastic properties are made to be linearly depen- 
dent on three field variables, FVl through FV3. 
The first field variable represents the matrix fail- 
ure, the second the fiber-matrix shearing failure, 
and the third the fiber buckling failure. The val- 
ues of the field variables are set to zero in the 
undamaged state. After a failure index has ex- 
ceeded 1.0, the associated user-defined field vari- 
able are set to 1.0. The associated field vari- 
able then continues to have the value of 1.0, even 
though the stresses may reduce to values lower 
than the failure stresses of the material. This pro- 
cedure ensures that the damaged material does 
not heal. The mechanical properties in the dam- 
aged area are reduced appropriately, according to 
the property degradation model defined in Table 
1. For example, when the matrix failure crite- 
rion takes the value of 1.0, then by the interpola- 
tion rule defined in Table 1, the transverse shear 
modulus (Ey) cind the Poisson ratio (1/12) axe set 
equal to zero. The field variables can be made to 
transit from (undamaged) to 1 (fully damaged) 
instantaneously. Chang and Lessard's degrada- 
tion model [4] is used in the present study. 

The finite element implementation of this 
progressive failure analysis was developed for 
the ABAQUS structural analysis program using 
the USDFLD user-written subroutine [12, 13]. 
ABAQUS calls this USDFLD subroutine at all 
material points of elements that have material 
properties defined in terms of the field variables. 
The subroutine provides access points to a num- 
ber of variables such as stresses, strains, mate- 
rial orientation, current load step, and material 
name, all of which can be used to compute the 
field variables. Stresses and strains are computed 
at each incremental load step and evaluated by 



the failure criteria to determine the occurrence of 
failure and the mode of failure. 

Numerical Examples 

To assess the predictive capability of the 
present failure analysis method, several panels 
have been analyzed and these results were com- 
pared with experimental results. Results are pre- 
sented for unstiffened panels with and without 
cutouts and a stiffened panel. The unstiffened 
panel cases are a flat panel loaded in shear and 
a curved panel loaded in compression. Results 
are also presented for a bead-stiffened panel sub- 
jected to in-plane shear loading. 

Flat Panel Loaded in In-plane Shear 

The panels subjected to pure in-plane shear 
loading were loaded using a picture frame fix- 
ture. The test sections of the bead-stiffened and 
unstiffened panel were 12.0 by 12.0 in. in size 
and the members of the picture frame were 2.75- 
in. wide and 6.75-in thick. The fixture is made 
of steel. Figure 1 shows a schematic diagram of 
a picture frame test fixture. In the finite ele- 
ment model, nodes on each member were con- 
strained for the out-of-plane displacement. Pin 
joint consists of two co-incident nodes tied in 
a multi-point constraint at the four corners of 
the panel. The displacements of the dependent 
node is made the same as that of the indepen- 
dent node, but the rotations of the co-incident 
nodes are excluded in the multi-point constraints. 
The independent node diagonally opposite to the 
loading pin is constrained for axial and transverse 
displacements. At the loading pin, applied dis- 
placement equal in magnitude in the axial and 
transverse directions at the independent node 
simulates the loading condition. The test section 
is modeled using ABAQUS four node, reduced 
integration, shear deformable S4R element [13]. 
The members of the picture frame are modeled 
using ABAQUS four node shear deformable S4 
element [13]. 

The flat unstiffened panel has a lami- 
nate stacking sequence of [±4o/0/90]2s, with 
a ply thickness of 0.0056-in. and is made 
of graphite epoxy. The mechanical properties 
for the material are £u = 18.5 Msi, £22 = 1-64 
Msi, Gi2=Gi3=0.87 Msi, G23=0.55 Msi, and 
1/12=0.3. The strength allowables are A't=232.75 
ksi, A'e=210.0 ksi, V; = 14.7 ksi, re=28.7 ksi, 
Sc:i2=29.75 Ksi, and 5ci3=5c23=4.8 ksi. Experi- 
mental results for this test panel are reported in 
Reference [14]. 



A finite element model of the panel is shown 
in Figure 2. This model consists of 3425 nodes 
and 3300 elements. An imperfection based on 
static analysis results for a pressure load was 
added to the model to simulate an imperfect 
shape similar to that of a bubble (one half wave 
in each direction of the panel). Progressive fail- 
ure analysis (PFA) was carried out for this case 
with a mciximum imperfection magnitude equal 
to 5% of the laminate thickness. Three integra- 
tion points through each ply thickness are used 
in the analysis for computation of section prop- 
erties. A post-buckling analysis of the panel 
with the same level of imperfection was also per- 
formed. 

The results for the flat pcuiel loaded in shear 
are shown in Figure 3, where the load is plotted 
versus the strain normal to the fiber direction 
(£22) in the top and bottom ply (45° ply) at the 
center of the test specimen. The dashed lines 
marked FVl, FV2 and FV3 indicate the load 
level at which damage described by field vari- 
able FVl through FV3 are initiated well into 
the post buckling regime. These failures are due 
to severe bending in the region. The thick solid 
line represents the experimental results and the 
thin solid line represents the postbuckling analy- 
sis results. The solid and open triangles are an- 
alytical results for the panel response that indi- 
cates progression of failure. The analysis results 
are in good agreement with the experimental re- 
sults. The final failure load obtained from the 
experiment is 54.81 kips, which is 6 % more than 
the final failure load of approximately 51.5 kips 
obtained from progressive failure analysis. Dam- 
age initiation starts as matrix cracking (FVl) at 
a load level of 37.76 kips. Fiber-matrix shear 
{FV2), and fiber (F73) failure are initiated at 
the same load level of 45.37 kips. This indicates 
that the structure can carry an additional 17.04 
kips (about 30% of the final experimental load) 
after matrix cracking has been initiated. Even af- 
ter the initiation of fiber-matrix shear and fiber 
failure, the panel continues to carry an additional 
load of about 9.4 kips ( 17% of the final experi- 
mental load). The post-buckling analysis results 
diverge from the progressive failure results at a 
load level that is slightly higher than the load at 
which initiation of fiber-matrix shear and fiber 
failure occurs. At that load level the analysis pre- 
dicts a significant amount of damage that could 
have led to a considerable loss of panel stiff'ness. 

All the failure modes initiated near the steel 
supporting fixture close to the region along the 



diagonal which is in the panel loading direction 
and propagate in the region close to the diagonal 
and along the loading direction. Figure 4 shows 
a fringe plot of matrix cracking (FVl) in the top 
ply after the final failure load. The dark contours 
denote failed regions of the panel. Other damage 
modes accumulate in approximately the same re- 
gion as depicted by the plot. These damage loca- 
tions are consistent with observations from exper- 
iments and do not involve delamination failure. 

Curved Panel Loaded in Axial Compression 

The curved panel has a laminate stacking 
sequence of [±45/0/90]3s, with a ply thickness 
of 0.005-in. The mechanical properties of the 
material used for the panel are £ii = 17.5 Msi, 
£22=1-51 Msi, Gi2=Gi3=0.78 Msi, ^23=0.55 
Msi, and 1^12=0.29. The strength allowables £u:e 
Xt=206.0 ksi, Xc=206.0 ksi, Yt=8.9 ksi, Yc=17.8 
ksi, 5ci2 = 18.3 Ksi, and 5ci3=Sc23=4.8 ksi. Ex- 
perimental results for this test are reported in 
Reference [15]. 

The panel geometry, boundary conditions 
and loading are shown in Figure 5. The panel 
finite element model consists of 6561 nodes and 
6400 elements. Measured geometric imperfection 
from a typical test specimen was included in the 
model. Three integration points through each ply 
thickness are used in the analysis for computation 
of section properties. 

The results for the curved panel loaded in 
compression are shown in Figure 6, where the 
load is plotted against the end shortening dis- 
placement. The filled symbols representing FVl, 
FV2, and FV3 indicate the load level at which 
damage described by field variable FVl through 
FV3 are initiated. The analysis and expermental 
results are in good agreement. The final failure 
load from the experiment is 51.25 kips, which is 
1 1 % less than the final failure load obtained from 
progressive failure analysis of about 56.8 kips. All 
damage modes initiate after the panel buckling 
and attaining its final load bearing capability. 
Matrix cracking {FVl) initiated at a load level 
of 43.31 kips just after buckling. Fiber-matrix 
shear (FV'2) and fiber failure (FV'3) initiated at 
a load level of 37.53 kips and a load level of 38.32 
kips, respectively. 

Figure 7(a) through 7(c) show fringe plots 
for matrix cracking (FVl), fiber matrix shear 
(FV2), and fiber failure (FV3) in the bottom ply 
after final failure at an applied displacement of 
approximately 0.1-in.. Damage initiated within 



than the experimental failure load. Damage initi- 
ation starts as fiber-matrix shear {FV2) and fiber 
(FV3) failure at the same load level of 28.34 kips. 
Matrix cracking {FVl) is initiated at a load level 
of 30.22 kips. Hence the curved panel can carry 
an additional load of about 11.0 kips (about 27% 
of the final experimental load) after initiation of 
fiber-matrix shear and fiber failure. After matrix 
cracking heis been initiated, the panel can carry 
an additional load of 9.0 kips (about 23% of the 
final experimental load). 

All the failure modes initiated near the edge 
of the cutout. Figure 12 shows a fringe plot for 
matrix cracking (FVl) in the bottom ply after 
the final failure load. These damage locations are 
consistent with experimental observations. How- 
ever experimental observation indicated signifi- 
cant delamination around the cutout. Although 
the initial geometric imperfection are accurately 
represented here, the delamination damage may 
be responsible for the discrepancy between the 
analytical and experimental failure loads with the 
panel exhibiting a catastrophic failure with no 
residual strength. 

Bead-stiffened Panel Loaded in Shear 

The thermoformed bead- stiffened configura- 
tion is an advanced concept for stiffened graphite 
thermoplastic panels. Thermoforming ia a cost 
effective manufacturing method for incorporat- 
ing bead stiffeners. An experimental and analyt- 
ical investigation of these bead-stiffened panels 
was conducted by Rouse [17]. The bead-stiffened 
panels were loaded in in-plane shear loading us- 
ing a picture frame fixture similar to the one de- 
scribed above. It was found that the bead stiflF- 
ened panels failed near the curved tip of the stiff- 
ener where large magnitudes of stress resultants 
were predicted. 

The bead-stiffened panel has a laminate 
stacking sequence of [±45/ ± 45/0/ ± 45/90]s 
with a ply thickness of 0.005-in. The mechan- 
ical properties of the material are £^u = 18.0 
Msi, £22=1.50 Msi, Gi2=Gi3=G23=0.82 Msi. 
The allowables are X(=300.0 ksi, Xc=210.0 ksi, 
Yt=l3.0 ksi, n=31.0 ksi, Sci2=27.0 Ksi, and 
5ci3=Sc23=5.0 ksi. A finite element model of 
the bead-stiflened panel is shown in Figure 13. 
This model consists of 2935 nodes and 2849 ele- 
ments. No geometric imperfection was added to 
the model of the bead-stiffened panel. Three in- 
tegration points through each ply thickness are 
used in the analysis for computation of section 
properties. 



The results for this in-plane shear-loaded 
panel are shown in Figure 14, where the load is 
plotted versus the axial strain {e^^x) in the top 
and bottom plies (45° ply) at the center of the 
test panel. The curves FVl, FV2, and FV3 in- 
dicate the load level at which damage modes de- 
scribed by the field variable FVl through FV3 
initiate. The analyses results sire in good agree- 
ment with the experimental results. The final 
failure load obtained from the experiment is 27.9 
kips, which is 12 % less than the final failure load 
obtained from the progressive failure analysis of 
about 24.4 kips. Damage initiation starts as ma- 
trix cracking (FVl) at a load level of 10.8 kips, 
whereas fiber-matrix shear {FV2) and fiber fail- 
ure are initiated at the same load level of 12.8 
kips. Hence the structure can carry an additional 
load of approximately 17.0 kips (60% of the final 
experimental load) after matrix cracking damage 
has been initiated. Even after initiation of fiber- 
matrix shear and fiber failure, the panel can carry 
an additional load of approximately 15.0 kips ( 
53% of the final experimental load). 

Figure 15(a) through 15(c) show fringe plots 
for matrix cracking, fiber-matrix shear, and fiber 
failure in the top ply after the final failure load. 
The damage initiated near the curved tip of the 
bead-stiflener and propagated to the other re- 
gions as shown in these figures. The locations 
for damage are consistent with experimental ob- 
servations. For the case of this stiffened panel, 
initial geometric imperfections are not a criticeJ 
factor in predicting the observed behavior. 

Concluding Remarks 

The results of an analytical and experimen- 
tal study to evaluate the initiation and progres- 
sion of damage in nonlinearly deformed stiffened 
sdid unstiffened panel are presented. These stud- 
ies are also conducted for panels with cutouts 
and subjected to two loading conditions. The 
progressive failure methodology includes matrix 
cracking, fiber-matrix shear, and fiber failure, 
but ignores delamination failure. The effect of 
initial geometric imperfections is also investi- 
gated as part of the study. 

For a flat panel loaded in in-plane shear load- 
ing, the three failure modes considered in the 
study accurately represent the damage senario in 
the postbuckling regime. The analytically deter- 
mined response, failure modes and damage loca- 
tions compare well with the experimental results 
when the initial geometric imperfection is in- 
cluded in the analysis in a simple manner. When 



6 



/■' >- ^, 



a cutout is introduced, however, delamination oc- 
curs at the hole boundary as an additional fail- 
ure mode resulting in some discrepancies with the 
observed behavior. The analysis results also pre- 
dict a residual strength with the final failure load 
being approximately 10% greater than the exper- 
imental failure load. 

The response of curved panels with and 
without cutouts are studied when loaded in com- 
pression. With measured geometric imperfection 
included in both curved panel models, the re- 
sponse of the panel without cutout compares well 
with experimental results. No delamination oc- 
curs for this case and the failure modes consid- 
ered in this paper develop after buckling. For 
the curved panel with a cutout, however delam- 
ination does occur with the panel failing catas- 
trophically. Unlike the panel without a cutout, 
this panel with a cutout exhibits no residual 
strength. It may be important to include de- 
lamination failure mode to predict the residual 
strength of curved panels with a cutout of the 
type considered here. 

The bead-stiffened panel response, failure 
modes and damage locations are well predicted 
by the analysis results. The residual strength val- 
ues from the analysis and experiment are within 
12 percent with no geometric imperfection in- 
cluded in the analysis. 



References 

[1] Talreja, R., "Modeling of Damage Develop- 
ment in Composites using Internal Variable 
Concepts," Damage Mechanics in Compos- 
ites, AD Vol. 12, Proceedings of the ASMS 
Winter Annual Meeting, Boston, MA, 1987, 
pp. 11-16. 

[2] Allen, D. H., Harris, C, and Groves, S. 
E., "A Thermomechanical constitutive The- 
ory for Elastic Composites with Distributed 
Damage, Part I. Theoretical Development," 
International Journal of Solids and Struc- 
tures, Vol. 23, No. 9, 1987, pp. 1301-1318. 

[3] Chang, F.-K., and Chang, K. Y., "A Pro- 
gressive Damage Model for Laminated Com- 
posites Containing Stress Concentrations," 
Journal of Composite Materials, Vol. 21, 
Sept. 1987, pp. 834-855. 



[4] Chang, F.-K., and Lesard, L. B., "Damage 
Tolerance of Laminated Composites Con- 
taining an Open Hole and Subjected to 
Compressive Loadings: Part 1-Analysis," 
Journal of Composite Materials, Vol. 25, 
Jan. 1991, pp. 2-43. 

[5] Davila, C. G., Ambur, D. R., and Mc- 
Gowan, D. M., "Analytical Prediction of 
Damage Growth in Notched Composite Pan- 
els Loaded in Compression," Journal of Air- 
craft, Vol. 37, No. 5, pp. 898-905. 

[6] Minnetyan, L., Chamis, C. C, and Murthy, 
P. L., "Damage and Fracture in Compos- 
ite Thin Shells," NASA TM-105289, Nov., 
1991. 

[7] Averill, R. C, "A Micromechanics-Based 
Progressive Failure Model for Laminated 
Composite Structures," Proceedings of 
the 33rd AIAA/ASME/ASCE/AHS/ASC 
Structures, Structural Dynamics, and Mate- 
rials Conference, AIAA, Washington, DC, 
1992, pp. 2898-2904. 

[8] Moas, E., "Progressive Failure Analysis of 
Laminated Composite Structures," Ph.D 
Dissertation, Engineering Mechanics Dept., 
Virginia Polytechnic Inst, and State Univ., 
Blackburg, VA 1996. 

[9] Sleight, D. W., Knight, N. F. Jr., and 
Wang, J. T., "Evaluation of a Progres- 
sive Failure Analysis Methodology for Lam- 
inated Composite Structures," Proceedings 
of the 38th AIAA/ASME/ASCE/AHS/ASC 
Structures, Structural Dynamics, and Ma- 
terials Conference, Reston, VA, 1997, pp. 
2257-2272. 

[10] Gummadi, L. N. B., and Palazotto, A. N., 
"Progressive failure Analysis of Composite 
Shells considering Large Rotations," Com- 
posite Part B, Vol. 29, 1998, pp. 547-563. 

[11] Hashin, Z., "Failure Criteria for Unidirec- 
tional Fiber Composites," Journal of Ap- 
plied Mechanics, Vol. 47, June 1980, pp. 329- 
334. 

[12] ABAQUS User's Manual, Vol. 3, Ver. 5.6, 
Hibbitt, Karlsson, and Sorensen, Pawtucket, 
RI, 1996, pp. 25.2.33-1. 

[13] ABAQUS Example Problems Manual, Vol. 
1, Ver. 5.5, Hibbitt, Karlsson, and Sorensen, 
Pawtucket, RI, 1995, pp. 3.2.25.25-1. 



[14] Rouse, M., "Post Buckling of Flat 
UnstifFened Graphite-Epoxy Plates 
Loaded in Shear," Presented at the 
AIAA/ASME/ASCE/AHS 26th Structures, 
Structural Dynamics, and Materials Confer- 
ence, Orlando, Florida, April 15-17, 1985. 
Also AIAA Paper No. 85-0771-CP. 

[15] Hiburger, M. W., Britt, V. 0., and 
Nemeth, M. P., "Buckling Behavior of 
Compression-loaded Quasi-isotropic Curved 
Panel with a Circular Cutout," 40th 
AIAA/ASME/ASCE/AHS/ASC Struc- 
tures, Structural Dynamics and Materials 
Conference, St. Louis, MO , Paper AIAA- 
99-1279, April 12-15, 1999. 

[16] Rouse, M., "Effect of Cutouts or Low-speed 
Impact Damage on the Postbuckling Behav- 
ior of Composite Plates Loaded in Shear," 
Presented at the AIAA/ASME/ASCE/AHS 
31th Structures, Structural Dynamics, and 
Materials Conference, Long Beach, Califor- 
nia, April 2-4, 1990. Also AIAA Paper No. 
90-0966-CP. 

[17] Rouse, M., "Structural Response of Bead- 
stiffened Thermoplastic Shear Webs," First 
NASA Advanced Composite Technology 
Conference, Oct. 29-Nov. 1, 1990., NASA 
Conference Publication 3104, pp. 969-977. 



Table 1: Dependence of material elastic 
properties on the field variables 



No Matrix 

failure cracking 



Fiber-matrix, 
shear 



Fiber 
failure 



En 


En 




En 


En ->0 


£/22 


E22 


->0 


■^22 


£^22 ^0 


1^12 


V12 


-^0 


1^12 ->o 


1/12 ^0 


Gi2 


Gn 




G12 ^0 


Gi2^0 


G,3 


Gl3 




Gi3 ->0 


Gi3 -^0 


G23 


G23 




G23 


G23 ^0 



FV'1=0 


FV'1 = 1 


FV'1=0 


FV'1=0 


fV'2=0 


FV'2=0 


FV2=l 


FV'2=0 


FV2=0 


FV'3=0 


FV'3=0 


FV3^l 



frame member 



\Z 



Loading 
direction 



1 



^ 



45 deg. 



test 



section 



frame 
member 



• Pin joint 



Figure 1 Schematic diagram of picture frame 
test fixture. 




Figure 2 Finite element model of a flat 

composite panel in the picture frame test 

fixture. 



Post-buckling 
analyses 




10000 



-8.02-0.015-0.01 -O.OOS 0.005 0.01 0.01 S 0.1 

strain (Ejj), inVin. 

Figure 3 Load vs. strain component normal to 

fiber direction in top and bottom plies of flat 

panel loaded in the picture frame test fixture. 




0.05 

End-shortening, in. 



Figure 6 Load vs. end-shortening displacement 
results for curved panel loaded in compression. 




Figure 4 Fringe plot for matrix cracking {FVl) 
in the top ply of the flat pcinel. 




Figure 7(a) Fringe plot for matrix cracking in 

the bottom ply for curved panel loaded in 

compression. 





Figure 7(b) Frmge plot for fiber-matrix shear in 
Figure 5 Geometry and boundary conditions for the bottom ply for curved panel loaded in 

curved composite panel. compression. 






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Figure 7(c) Fringe plot for fiber failure in the 

bottom ply for curved panel loaded in 

compression. 





Figure 10 Fringe plot for fiber failure in the top 

ply for the flat panel with a cutout loaded in 

the picture frame test fixture. 



Failure 



Figure 8 Finite element model of flat panel with 
a circular cutout. 




0.02 0.04 0.06 

End-shortening, In. 



0.12 



0,# Experiment 

A, A 1%t Imperfection 

D,l 5%t Impeilectlon 




Figure 11 Load versus end-shortening 
displacement for a curved panel with cutout 
{d/W=0.2) and subjected to axial compression 
loading. 



Figure 9 Load vs. strain component normal to 

fiber direction in the top and bottom plies of 

flat panel with a cutout loaded in the picture 

frame test fixture. 




Figure 12: Plot for matrix cracking damage in 

the bottom ply for curved panel with cutout 

{d/W-Q.2) and loaded in compression. 



10 





Figure 13: Finite element model of the 

bead-stiffened panel in picture frame test 

fixture. 



Figure 15(b) Fringe plot for fiber-matrix shear 
in the top ply of the bead-stiffened panel 




top ply 



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Strain (E„) 

Figure 14: Load versus axial strain, (en) results 
at the center of bead-stiffened panel. 



Figure 15(c) Fringe plot for fiber failure in the 
top ply of the bead-stiffened panel 





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Figure 15(a) Fringe plot for matrix cracking in 
the top ply of the bead-stiffened panel 



11 



July 26, 2001 
NASA STI Acquisitions DAA Authorization 

The following papers (copies enclosed) have been DAA approved as Unclassified, Publicly Avail- 
able documents: 

Meeting Presentations: nm c \>j\ 

42nd AIAA/ASME/ASCE/AHS Structures, Structural Dyn..., 4/16-19/2001, Seattle, WA: 

TF Johnson et al ■ High Temperature Polyimide Materials in Extreme Temperature... 

D A Russell,' er al.: Effects of Electrons, Proton, and Ultraviolet Radiation on Thermo... 

J Arbocz et al ■ On the Accuracy of Probabilistic Buckling Load Predictions. 

j' Arbocz! et al.: On a High-Fidelity Hierarchical Approach to Buckling Load Calculations. 

M P Nemeth: Buckling Behavior of Long Anisotropic Plates Subjected to Fully 

D R Ambur et al : Progressive Failure Studies of Composite Panels With and Without... 

M W. Hilburger, et al.: High-Fidelity Nonlinear Analysis of Compression-Loaded... 

M W Hilburger, et al.: Nonlinear Analysis and Scaling Laws for Noncircular Composite 

M w' Hilburger, et al.: NonUnear and Buckling of Curved Panels Subjected to Combined... 

J C Newman, et al. : A Review of the CTOA/CTOD Fracture Criterion - Why it Works 
10th AlAA/NAL-NASDA-ISAS Int'l Space Plane & Hypersonic..., 4/24-27/2001, Kyoto, Japan: 

C R McClinton, et al.: Hyper-X Program Status. 
American Helicopter Society 57th Annual Forum, 5/9-1 1/2001, Washington, DC: 

M L Wi^ur .r al ■ Vibmtoiy Loads Reduction Testing of the NASA/ARMY/MIT Active... 
7th AlAA/CEAS Aeroacousiics Conference, 5/28-30/2001, Maastricht, The Netherlands: 

L Maestrello: Laminarization of Turbulent Boundary Layer on Flexible and Rigid Structures. 
15th AlAA Computational Fluid Dynamics, 6/11-14/2001, Anaheim, CA: 

D. Sidilkover, et al.: Factorizable Upwind Schemes: The Triangular Unstructured Grid... 

Susan H. Stewart 

^» . r. . ,■ ,^ s.h.stewart@larc.nasa.gov 

DAA Representative ^- n^n\9.(^ l^\9, 

Hampton, VA 23681-2199